Interactions and self-healing of Cu vias during stress migration tests and implications for burn-in and design rule formulations

During High Temperature Storage (HTS), previously failed vias due to open failures from voids subsequently self-heal. Likewise, the resistance shifts appear to saturate and reverse direction over long times. The propensity for self-healing and subsequent “immortality” can be explained in a physical model by an interaction between voids and material sinks (such as grain boundaries) analogous to growing second-phases in late-stage precipitation - also called Ostwald ripening. HTS data is collected from a 130 nm Cu/low-k BEOL process, with various geometrical variations, single and multiple vias, initial resistances and processing. Resistance shifts and open failures are tracked and modeled. The model is based on formulating a mean-field, which is the volume averaged stress due to the arrays of voids and the material shed during their growth. This model takes into account the surface energy of the growing void through the sintering stress as a boundary condition. A key outcome of this formulation is a critical void radius in equilibrium with the mean stress, where, voids with a supercritical radius will grow at the expense of voids with subcritical radius. The maximum void size is modified by the surface energy and the elastic modulus. We show that the saturated void radius (SVR) is truly an upper bound on the size of any particular void. We demonstrate the implications for reliability and engineering design through scaling relationships well as indicate directions for further experimental and theoretical study.